The US Embassy in Ireland has confirmed that dual nationals of the countries listed in the US Executive Order who are not eligible for the Visa Waiver Program can now again apply for visas to travel to the US.
Those affected had been advised not to present themselves at the embassy with an application or pay any visa fees.
The embassy said that following further guidance from Washington, people from the listed countries with dual nationality can apply for a visa.
Taoiseach Enda Kenny earlier told the Dáil that 5,000 people from the seven countries have Irish citizenship and live in Ireland and are entitled to be admitted to the US if they present their Irish passports.
The US Embassy in Ireland said on its website that there are no changes to the visa waiver programme, but "as before dual nationals of Iraq, Iran, Syria, and Sudan are not eligible for the Visa Waiver Program and must have a visa for travel".
It said that the executive order signed by Mr Trump on Friday "does not restrict the travel of dual nationals, so long as they hold the passport of an unrestricted country and possess a valid US visa".
It added that "dual nationals of Yemen, Libya, and Somalia and a VWP country may continue to travel under the VWP unless they have travelled to any of the seven countries on or after March 2011, in which case they must first apply for a US visa".
In a statement this evening, the Embassy said that "our Embassies and Consulates around the world will process visa applications and issue nonimmigrant and immigrant visas to otherwise eligible visa applicants who apply with a passport from an unrestricted country, even if they hold dual nationality from one of the seven restricted countries".
Meanwhile, US Homeland Security Secretary John Kelly has said his officials will continue to enforce the travel ban on citizens from seven Muslim-majority countries "humanely".
However, he added that some of the countries affected will not likely be taken off the list any time soon.
Mr Kelly said people from the seven countries who hold dual citizenship will be allowed enter the US on the passport of a non-restricted nation.
Over the weekend, US President Donald Trump put a 120-day hold on allowing refugees into the US, an indefinite ban on refugees from Syria and a 90-day bar on citizens from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen.
There was widespread confusion at airports around the world as customs officials and airlines struggled to interpret the new rules.
Several lawsuits have been filed blocking portions of the order, which drew harsh criticism from Democrats, human rights organisations and some US allies.
Since the order, 721 travellers trying to enter from the seven countries were denied entry, according to Kevin McAleenan, acting commissioner of Customs and Border Protection.
Mr Kelly said federal immigration and customs officials were in compliance with the court orders on immigration and no agent knowingly or intentionally violated them.
Meanwhile, Swiss dual citizens with valid visas have been exempted from the temporary travel ban, Switzerland's foreign ministry said.
"Swiss dual citizens who are additionally citizens of Iraq, Iran, Syria, Libya, Sudan, Somalia or Yemen are once again allowed to travel to the United States with immediate effect, provided they have a valid visa in their Swiss passport," the ministry said in a statement after talks with US authorities.
Such Swiss dual citizens would not be able to travel to the United States without already having a valid visa because they cannot now apply for one, it added, citing US officials.
